The structure represent thymine because of the characteristic carbonyl groups at both carbons 2 and 4 and the methyl group at carbon 5.

The structure represents uracil because of the carbonyl groups attached to both carbons 2 and 4 and the lack of any other substituents.

The structure represents cytosine because of the characteristic amine group on carbon 4, instead of the carbonyl group that is present on carbon 4 of both thymine and uracil.

Pyrimidines are nitrogenous bases with 1 ring structure, whereas purines are nitrogenous bases with 2 ring structures. Cytosine and thymine are pyrimidines since they both have one ring structure, whereas adenine and guanine are purines with two connected ring structures. (Note: in RNA, uracil would be considered a pyrimidine in the place of thymine.) One way to help you remember which bases belong to which chemical groups, remember that pyrimidines, like pyramids are sharp, and sharp things CUT - Cytosine, Uracil, and Thymine.

The six-membered ring is a pyrimidine. The purine ring system has two rings: a six-membered and a five-membered ring. These aromatic rings are hydrophobic, making them relatively insoluble. The pyrimidine bases in nucleotides are cytosine, uracil, and thymine; the purine bases in nucleotides are adenine and guanine.

A nucleoside is the nitrogenous base bound to a sugar via glycosidic bond. A nucleotide is a nitrogenous base bonded to a sugar bonded to the phosphate. This nitrogenous base is cytosine. If it were bound to ribose, it would be called cytidine. Although cytosine is a pyrimidine like uracil and thymine, pyrimidine is a class of ring structure, not the specific name of a base. 

While adenine is the name of this nitrogenous base of the purine family, when bonded to ribose, a nucleoside is formed. This nucleoside is called adenosine. A nucleoside consists of a nitrogenous base and a pentose sugar (either ribose or deoxyribose). A nucleotide consists of a nitrogenous base, a pentose sugar, and at least one phosphate group.

When the guanine base is bound to a sugar, it becomes a nucleoside and takes the name guanosine. The 5' indicates that the phosphate is bound to the fifth carbon from the glycosidic bond, linking the base and sugar. Monophosphate indicates that only one phosphate group is bound. Up to three phosphate groups are be bound biologically.

This is an image of the nitrogenous base uracil. Although very similar to the structure of thymine, they differ by a methyl group at the fifth carbon. (Start counting at the nitrogen at the bottom of the structure and count clockwise). If the uracil were bound to a sugar, it would be uridine.

This nitrogenous base is adenine. Although it has a purine ring system, purine is not its specific name. If the adenine were bound to a sugar, it would be called adenosine.